In storage modules with memory cells that can store more than one bit per cell, a lower page of data is first written in the memory cells, and then later, an upper page of data is written in the memory cells. In the process of writing the upper page of data in the memory cells, the previously-written values in the memory cells for the lower page are changed. So, if a power loss occurs during upper-page programming, the lower page of data may be lost because the upper-page programming of the cells corrupts the lower-page values previously stored in the cells. To guard against this possibility, the lower page of data can be backed up to another area of the memory (sometimes referred to as a “safe zone”) before the upper page is written. That way, if there is a power loss when writing the upper page, the lower page can be restored from the backup. While backing-up a previously-written lower page protects against data loss if there is a power loss, backing up lower pages every time an upper page is written can reduce the performance of the storage module and provide excessive wear to the memory cells.